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7th grade math

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I hope this makes sense, but my teacher said he wants all exponents in the prime factorization, the example he gave was,
4^2
he wants 2^4
Is there a simple way to figure it out? for example, i'm trying to figure out 10^4.

  • 7th grade math -

    Prime factorization just means breaking any number into prime numbers.

    10^4= 10,000. The easiest method is to just divide this number my prime numbers until it can't be divided any further. It's a good idea to start dividing with the smallest primes, like 2.

    10,000/2=5,000
    5,000/2=2,500
    2,500/2=1,250
    1,250/2=625
    -Alright once we divided by 2, the smallest prime, 4 times, we can no longer continue dividing by 2, so we move onto larger primes. 3 does not divide evenly into 625, but 5 does.
    625/5=125
    125/5=25
    25/5=5
    5/5=1
    -Ok, we can stop now because no prime we try will divide evenly into 1.

    So we divided by 4 four times, and divided by 5 four times. Basically:
    2*2*2*2*5*5*5*5=10^4 (10,000)
    do
    2^4*5^4=10^4

    So the prime factorization is: (2^4)*(5^4)

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